Integration of One-forms on P-adic Analytic Spaces. (AM-162) /
Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place. For example, a closed p-adic analytic one-form defined on a simply-connected domain does not necessarily have a primitive in the class of analytic functions. In the early...
Clasificación: | Libro Electrónico |
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Autor principal: | |
Formato: | Electrónico eBook |
Idioma: | Inglés |
Publicado: |
Princeton, NJ :
Princeton University Press,
[2006]
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Edición: | Course Book |
Colección: | Annals of Mathematics Studies ;
162 |
Temas: | |
Acceso en línea: | Texto completo Texto completo |
MARC
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100 | 1 | |a Berkovich, Vladimir G., |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 0 | |a Integration of One-forms on P-adic Analytic Spaces. (AM-162) / |c Vladimir G. Berkovich. |
250 | |a Course Book | ||
264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2006] | |
264 | 4 | |c ©2007 | |
300 | |a 1 online resource (168 p.) : |b 14 line illus. | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a Annals of Mathematics Studies ; |v 162 | |
505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Introduction -- |t 1. Naive Analytic Functions and Formulation of the Main Result -- |t 2. Étale Neighborhoods of a Point in a Smooth Analytic Space -- |t 3. Properties of Strictly Poly-stable and Marked Formal Schemes -- |t 4. Properties of the Sheaves Ω1.dx/dOX -- |t 5. Isocrystals -- |t 6. F-isocrystals -- |t 7. Construction of the Sheaves SλX -- |t 8. Properties of the sheaves SλX -- |t 9. Integration and Parallel Transport along a Path -- |t References -- |t Index of Notation -- |t Index of Terminology |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
520 | |a Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place. For example, a closed p-adic analytic one-form defined on a simply-connected domain does not necessarily have a primitive in the class of analytic functions. In the early 1980s, Robert Coleman discovered a way to construct primitives of analytic one-forms on certain smooth p-adic analytic curves in a bigger class of functions. Since then, there have been several attempts to generalize his ideas to smooth p-adic analytic spaces of higher dimension, but the spaces considered were invariably associated with algebraic varieties. This book aims to show that every smooth p-adic analytic space is provided with a sheaf of functions that includes all analytic ones and satisfies a uniqueness property. It also contains local primitives of all closed one-forms with coefficients in the sheaf that, in the case considered by Coleman, coincide with those he constructed. In consequence, one constructs a parallel transport of local solutions of a unipotent differential equation and an integral of a closed one-form along a path so that both depend nontrivially on the homotopy class of the path. Both the author's previous results on geometric properties of smooth p-adic analytic spaces and the theory of isocrystals are further developed in this book, which is aimed at graduate students and mathematicians working in the areas of non-Archimedean analytic geometry, number theory, and algebraic geometry. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) | |
650 | 0 | |a Analyse p-adique. | |
650 | 0 | |a p-adic analysis. | |
650 | 7 | |a MATHEMATICS / Geometry / Non-Euclidean. |2 bisacsh | |
653 | |a Abelian category. | ||
653 | |a Acting in. | ||
653 | |a Addition. | ||
653 | |a Aisle. | ||
653 | |a Algebraic closure. | ||
653 | |a Algebraic curve. | ||
653 | |a Algebraic structure. | ||
653 | |a Algebraic variety. | ||
653 | |a Allegory (category theory). | ||
653 | |a Analytic function. | ||
653 | |a Analytic geometry. | ||
653 | |a Analytic space. | ||
653 | |a Archimedean property. | ||
653 | |a Arithmetic. | ||
653 | |a Banach algebra. | ||
653 | |a Bertolt Brecht. | ||
653 | |a Buttress. | ||
653 | |a Centrality. | ||
653 | |a Clerestory. | ||
653 | |a Commutative diagram. | ||
653 | |a Commutative property. | ||
653 | |a Complex analysis. | ||
653 | |a Contradiction. | ||
653 | |a Corollary. | ||
653 | |a Cosmetics. | ||
653 | |a De Rham cohomology. | ||
653 | |a Determinant. | ||
653 | |a Diameter. | ||
653 | |a Differential form. | ||
653 | |a Dimension (vector space). | ||
653 | |a Divisor. | ||
653 | |a Elaboration. | ||
653 | |a Embellishment. | ||
653 | |a Equanimity. | ||
653 | |a Equivalence class (music). | ||
653 | |a Existential quantification. | ||
653 | |a Facet (geometry). | ||
653 | |a Femininity. | ||
653 | |a Finite morphism. | ||
653 | |a Formal scheme. | ||
653 | |a Fred Astaire. | ||
653 | |a Functor. | ||
653 | |a Gavel. | ||
653 | |a Generic point. | ||
653 | |a Geometry. | ||
653 | |a Gothic architecture. | ||
653 | |a Homomorphism. | ||
653 | |a Hypothesis. | ||
653 | |a Imagery. | ||
653 | |a Injective function. | ||
653 | |a Irreducible component. | ||
653 | |a Iterated integral. | ||
653 | |a Linear combination. | ||
653 | |a Logarithm. | ||
653 | |a Marni Nixon. | ||
653 | |a Masculinity. | ||
653 | |a Mathematical induction. | ||
653 | |a Mathematics. | ||
653 | |a Mestizo. | ||
653 | |a Metaphor. | ||
653 | |a Morphism. | ||
653 | |a Natural number. | ||
653 | |a Neighbourhood (mathematics). | ||
653 | |a Neuroticism. | ||
653 | |a Noetherian. | ||
653 | |a Notation. | ||
653 | |a One-form. | ||
653 | |a Open set. | ||
653 | |a P-adic Hodge theory. | ||
653 | |a P-adic number. | ||
653 | |a Parallel transport. | ||
653 | |a Patrick Swayze. | ||
653 | |a Phrenology. | ||
653 | |a Politics. | ||
653 | |a Polynomial. | ||
653 | |a Prediction. | ||
653 | |a Proportion (architecture). | ||
653 | |a Pullback. | ||
653 | |a Purely inseparable extension. | ||
653 | |a Reims. | ||
653 | |a Requirement. | ||
653 | |a Residue field. | ||
653 | |a Rhomboid. | ||
653 | |a Roland Barthes. | ||
653 | |a Satire. | ||
653 | |a Self-sufficiency. | ||
653 | |a Separable extension. | ||
653 | |a Sheaf (mathematics). | ||
653 | |a Shuffle algebra. | ||
653 | |a Subgroup. | ||
653 | |a Suggestion. | ||
653 | |a Technology. | ||
653 | |a Tensor product. | ||
653 | |a Theorem. | ||
653 | |a Transept. | ||
653 | |a Triforium. | ||
653 | |a Tubular neighborhood. | ||
653 | |a Underpinning. | ||
653 | |a Writing. | ||
653 | |a Zariski topology. | ||
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